Question

find the measure of ∠lon.

Explanation:

Step1: Recall the full angle at a point

A full angle around a point is \( 360^\circ \), but here we have three angles around point \( O \): \( \angle LOM = 68^\circ \), \( \angle MON = 94^\circ \), and \( \angle LON \) which we need to find. Wait, actually, no—wait, the sum of angles around a point is \( 360^\circ \), but maybe these are adjacent angles forming a full angle? Wait, no, looking at the diagram, the three rays \( OL \), \( OM \), \( ON \) are from point \( O \), so the sum of \( \angle LOM \), \( \angle MON \), and \( \angle LON \)? Wait, no, maybe I misread. Wait, actually, the angle around a point is \( 360^\circ \), but if we consider the straight line? No, the diagram shows three rays: \( OL \), \( OM \), \( ON \), with \( \angle LOM = 68^\circ \), \( \angle MON = 94^\circ \), so the remaining angle \( \angle LON \) can be found by subtracting the sum of the other two from \( 360^\circ \)? Wait, no, that can't be. Wait, maybe it's a full angle? Wait, no, maybe the three angles are around point \( O \), so \( \angle LOM + \angle MON + \angle LON = 360^\circ \)? Wait, no, that would be if they are all around the point. Wait, let's check: the sum of angles around a point is \( 360^\circ \). So if we have \( \angle LOM = 68^\circ \), \( \angle MON = 94^\circ \), then \( \angle LON = 360^\circ - 68^\circ - 94^\circ \)? Wait, no, that would be if they are the only three angles. Wait, maybe the diagram is such that the three angles form a full circle? Wait, no, maybe I made a mistake. Wait, let's recalculate: \( 360 - 68 - 94 = 198 \)? No, that doesn't seem right. Wait, maybe the angles are adjacent and form a full angle? Wait, no, maybe the diagram is a typo, or I misinterpret. Wait, no, wait: maybe the three angles are \( \angle LOM = 68^\circ \), \( \angle MON = 94^\circ \), and \( \angle LON \) is the angle we need, so the sum of all three around point \( O \) is \( 360^\circ \). So \( \angle LON = 360^\circ - 68^\circ - 94^\circ \). Let's compute that: \( 68 + 94 = 162 \), then \( 360 - 162 = 198 \). Wait, but that seems large. Alternatively, maybe the diagram is a straight line? No, the rays are \( OL \), \( OM \), \( ON \), so they are three rays from \( O \), forming three angles. Wait, maybe the problem is that the sum of angles around a point is \( 360^\circ \), so we subtract the two given angles from \( 360^\circ \) to get \( \angle LON \).

Step2: Calculate the sum of the given angles

First, add \( 68^\circ \) and \( 94^\circ \): \( 68 + 94 = 162^\circ \).

Step3: Subtract from \( 360^\circ \)

Now, subtract this sum from \( 360^\circ \): \( 360 - 162 = 198^\circ \). Wait, but that seems like a reflex angle. Maybe the diagram is different? Wait, maybe I misread the angles. Wait, the diagram shows \( \angle LOM = 68^\circ \), \( \angle MON = 94^\circ \), so the angle between \( OL \) and \( ON \) is \( 360 - 68 - 94 = 198^\circ \). Alternatively, maybe the angles are on a straight line? No, three rays can't be on a straight line. So the correct calculation is \( 360 - 68 - 94 = 198 \).

Answer:

\( 198^\circ \)